$\begingroup$Could it be that there are a couple mistakes in your equations, namely in $\ddot{y}$ you both multiply and divide by $m$ and shouldn't $\ddot{\theta}$ be a function of the difference of the inputs? Also what have you tried?$\endgroup$
– fibonaticMay 20 at 10:48

$\begingroup$yes you are right. Thanks.$\endgroup$
– npkpMay 20 at 19:03